A fully classical truth theory characterized by substructural means

PAILOS, FEDERICO MATÍAS

REVIEW OF SYMBOLIC LOGIC

CAMBRIDGE UNIV PRESS

Lugar: Cambridge; Año: 2019

1755-0203

In this paper, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to distinguish Classical Logic from ST, but also to some other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics which will need to be modified in light of the present investigation, according to which two logics can be non-identical even if they share the same valid inferences